Studying viscoelasticity in soft tissues with supersonic shear imaging

In this work, a 3D analytical formulation of the mechanical Green’s function in a viscoelastic medium is derived and presented. Based on a Voigt model to take into account viscoelasticity, this mathematical formulation is validated experimentally using the supersonic shear imaging technique (SSI). Taking benefit of the ultrasonic remote generation of a moving shear source radiating low‐frequency shear waves in the medium, this technique has been studied and validated for soft tissue elasticity mapping in previous works. It is shown here that the spatial and temporal shape of shear waves induced in soft tissues using SSI can be accurately modeled with the viscoelastic Green’s function. The influences of important parameters such as viscosity, elasticity, or diffraction on the shear wave shape are carefully studied and discriminated. In a second part, taking advantage of the previous modeling, the inverse problem consisting of recovering shear elasticity and viscosity is presented and validated using the Green’s function‐based simulation tool. Experiments on tissue‐mimicking phantoms presenting different viscoelastic properties are presented. The influence of out‐of‐plane shear propagation on the inversion algorithm is discussed.